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New Dialogues: Entanglement, Renormalization & Holography

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New Dialogues: Entanglement, Renormalization & Holography New Dialogues: Entanglement, Renormalization & Holography Chandrasekhar Lecture ICTS, December 10, 2014 Connections: New Dialogues: Entanglement, A New Synthesis: Renormalization & Holography Chandrasekhar Lecture ICTS, December 10, 2014 New Collisions In Physics : Entanglement, Renormalization & Holography Chandrasekhar Lecture ICTS, December 10, 2014 New Collisions In Physics : RemalizHi\, Holographn & Entangme Chandrasekhar Lecture ICTS, December 10, 2014 New Collisions In Physics : Entanglement, Renormalization & Holography Chandrasekhar Lecture ICTS, December 10, 2014 Physics of the 20th century: A grand synthesis of diverse ideas! 1927 Solvay Conference on Quantum Mechanics in the middle of the “collision”: Do these people look happy? 1927 Solvay Conference on Quantum Mechanics in the middle of the “collision”: Do these people look happy? Physics of the 20th century: A grand synthesis and progression of ideas! New Collisions in Theoretical Physics: Quantum Field Theory Statistical Mechanics Renormalization Particle Physics Group Many Body Theory String Theory Entanglement Holography Quantum Information Condensed Matter Gravity Theory Renormalization: microscopic constituents Renormalization: microscopic constituents merge to produce new collective effects merge to produce new collective effects on macroscopic scales Renormalization Group Wikipedia: “mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales” Universality: physics at long distances is largely insensitive to details of physics at short distances Renormalization Group Wikipedia: “mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales” Universality: physics at long distances is largely insensitive to details of physics at short distances Why Physics Works! NOT Our World: 12 seconds! The heck with loop quantum gravity. We’ll have to try a string theory approach. Renormalization Group Flows Wikipedia: “mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales” Effects of short-distance physics is absorbed in values of a few parameters of an effective theory RG Flows describe how parameters of a quantum field theory change as more and more degrees of freedom at different scales are methodically “integrated out” Renormalization Group Flows Wikipedia: “mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales” Effects of short-distance physics is absorbed in values of a few parameters of an effective theory RG Flows describe how parameters of a quantum field theory change as more and more degrees of freedom at different scales are methodically “integrated out” fixed points: flow is stationary “critical phenomena” Renormalization Group Flows Wikipedia: “mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales” Effects of short-distance physics is absorbed in values of a few parameters of an effective theory RG Flows describe how parameters of a quantum field theory change as more and more degrees of freedom at different scales are methodically “integrated out” fixed points: flow is stationary “critical phenomena” Conformal Field Theory (CFT): QFT with few dimensionless couplings; scale invariant theory New Collisions in Theoretical Physics: Quantum Field Theory Statistical Mechanics Renormalization Particle Physics Group Many Body Theory String Theory Entanglement Quantum Information Condensed Matter Gravity Theory Holography Holography • idea in quantum gravity has its origins in trying to understand paradoxes related to the realization that black holes are thermal systems emitting (almost) blackbody radiation • Bekenstein and Hawking: black hole horizons carry entropy!! thermodynamics relativity geometry quantum gravity Holography • idea in quantum gravity has its origins in trying to understand paradoxes related to the realization that black holes are thermal systems emitting (almost) blackbody radiation • Bekenstein and Hawking: black hole horizons carry entropy!! thermodynamics relativity geometry quantum gravity • window into quantum gravity?!? Holography • idea in quantum gravity has its origins in trying to understand paradoxes related to the realization that black holes are thermal systems emitting (almost) blackbody radiation • Bekenstein and Hawking: black hole horizons carry entropy!! thermodynamics relativity geometry quantum gravity • window into quantum gravity?!? • quantum gravity provides a fundamental scale Holography • idea in quantum gravity has its origins in trying to understand paradoxes related to the realization that black holes are thermal systems emitting (almost) blackbody radiation • Bekenstein and Hawking: black hole horizons carry entropy!! • quantum gravity provides a fundamental scale Holography • idea in quantum gravity has its origins in trying to understand paradoxes related to the realization that black holes are thermal systems emitting (almost) blackbody radiation • Bekenstein and Hawking: black hole horizons carry entropy!! • is really really small: (LHC: ) • get really big entropies!! big bag of hot gas: black hole: Holography • idea in quantum gravity has its origins in trying to understand paradoxes related to the realization that black holes are thermal systems emitting (almost) blackbody radiation • Bekenstein and Hawking: black hole horizons carry entropy!! • reminds us that entropy is associated with “heat” black hole thermodynamics • statistical mechanics also says: black hole microstates Holography • idea in quantum gravity has its origins in trying to understand paradoxes related to the realization that black holes are thermal systems emitting (almost) blackbody radiation • Bekenstein and Hawking: black hole horizons carry entropy!! • statistical mechanics also says: black hole microstates “holography” suggests that the horizon is a surface that encodes information about microstates but also that dynamics and evolution of black hole can be described in terms of an effective theory living on the horizon ( ‘t Hooft; Susskind) AdS/CFT Correspondence: Bulk: Boundary: • quantum gravity • quantum field theory • negative cosmological constant • no scale (at quantum level) • d+1 spacetime dimensions • d spacetime dimensions • no gravity! anti-de Sitter conformal space field theory (Maldacena ‘97) AdS/CFT Correspondence: Bulk: Boundary: • quantum gravity • quantum field theory • negative cosmological constant Holography • no scale (at quantum level) • d+1 spacetime dimensions • d spacetime dimensions • no gravity! anti-de Sitter conformal space field theory radius energy (Maldacena ‘97) (Freedman, Gubser, Pilch & Warner) Holographic RG flows: (Girardello, Petrini, Porrati & Zaffaroni) • imagine potential has stationary points giving negative cosmological constant • the gravity solution is AdS space – dual to a particular CFT ● ● ● (Freedman, Gubser, Pilch & Warner) Holographic RG flows: (Girardello, Petrini, Porrati & Zaffaroni) • imagine potential has stationary points giving negative cosmological constant • the gravity solution is AdS space – dual to a particular CFT • Holographic RG flows are solutions starting at one stationary point at large radius and ending at another at small radius – connects two CFTs between high and low energies ● ● UV IR ● Holographic RG flows: fixed points (CFT’s) = AdS spacetimes RG flows = geometries interpolating between asymptotic AdS regions New Collisions in Theoretical Physics: Quantum Field Theory Statistical Mechanics Renormalization Particle Physics Group Holographic RG Flows Many Body Theory String Theory Holography Quantum Information Condensed Matter Gravity Theory Quantum Entanglement • different subsystems are correlated through global state of full system Einstein-Podolsky-Rosen Paradox: • properties of pair of photons connected, no matter how far apart they travel “spukhafte Fernwirkung” = spooky action at a distance Quantum Information: entanglement becomes a resource for (ultra)fast computations and (ultra)secure communications Condensed Matter: key to “exotic” phases and phenomena, e.g., quantum Hall fluids, unconventional superconductors, quantum spin fluids, . Quantum Entanglement • different subsystems are correlated through global state of fully system Einstein-Podolsky-Rosen Paradox: • properties of pair of photons connected, no matter how far apart they travel “spukhafte Fernwirkung” = spooky action at a distance compare: No Entanglement!! Entangled!! Entanglement Entropy: • general diagnostic: divide quantum system into two parts and use entropy as measure of correlations between subsystems • procedure: • divide system into two subsystems, eg, A and B • trace over degrees of freedom in subsystem B • remaining dof in A are described by a density matrix • calculate von Neumann entropy: compare: No Entanglement!! Entangled!! Entanglement Entropy: • general diagnostic: divide quantum system into two parts and use entropy as measure of correlations between subsystems • procedure: • divide system into two subsystems, eg, A and B • trace over degrees of freedom in subsystem B • remaining dof in A are described by a density matrix • calculate von Neumann entropy: compare: New Collisions in Theoretical Physics: Quantum Field Theory Statistical Mechanics Renormalization Particle Physics Group
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